Impossible,Improbable or YA Its Doable

I am sure this is being monitored -So for conversation sake/hypothetical free speech and educational purposes only . Basically looking for the steps to remain unidentifiable as mush as possible. A step by step guide with backedup information that can show that a computer / laptop gives off this information when connecting to the internet and what to do to avoid such.? For the paranoid--do we know that Intel or AMD,or other parts of the machine are not encoding their chips / equiptment to give off identifying info of that machine or other parts of the machine that give off identifying that is traceable.

Question Are:

1) If a person wants to use a laptop on a open cafe / restaurant free wifi connection to try and hack someones gmail with bruteforce, what will be captured from the laptop by the connections and gmail servers? Meaning forensically , what signatures are given off by that laptop? That could be used later to trace this laptop? What is being recorded by the Cafe wifi and/or service provider(ISP)

2) Do you screw yourself by buying a laptop on line with credit cards-I am guessing yes as they us a transaction that is traceable and that card is tied to that laptop with some identifying serial number? OR Go the cash route on craiglists or electronic swap for cash-A burner laptop if you will?

3) Should you turn off the internal wifi and get a cash bought wifi card or antenna to use?

4)Correct to assume you can never use that laptop on you own home network again? Also, cannot use that Wifi card / antenna again?

5)Given that the internet as seen in the media is a total collection is using a service like REVERSE.NET supposedly run by like minded hackers any better then just using other connections?